Renormalization of Very Special Relativity gauge theories

Abstract

Mandelstam-Leibbrandt(ML) regularization of Very Special Relativity (VSR) amplitudes in momentum space depends on two fixed null vectors $n_{\mu },{\bar{n}}_{\mu }$ besides external momenta. ML is known to preserve gauge invariance and naive power counting. The second null vector ${\bar{n}}_{\mu }$ destroys the $Sim(2)$ symmetry of the VSR model. We devise a systematic procedure to take the ${\bar{n}}_{\mu }->0$ limit to recover the lost $Sim(2)$ symmetry. The procedure produces $Sim(2)$ and gauge invariant loop amplitudes. We show how to use this method to remove unphysical terms from the Non Relativistic Potential of Very Special Relativity Quantum Electrodynamics(VSR QED) with a massive photon. Then we compute the one loop renormalization of VSR QED. Finally we derive the anomalous magnetic moment of the electron, modified by neutrino and photon mass; and comments on the phenomenological implications.

25 pages, 13 figures, latex

References in corpus (11)

• Very Special Relativity
• General Very Special Relativity is Finsler Geometry
• Tenth-Order Electron Anomalous Magnetic Moment --- Contribution of Diagrams without Closed Lepton Loops
• Very special relativity as relativity of dark matter: the Elko connection
• On the consistency of Lorentz invariance violation in QED induced by fermions in constant axial-vector background
• SIM(2)-invariant Modifications of Electrodynamic Theory
• Electroweak standard model with very special relativity
• Sim(2) and SUSY
• Very Special Relativity in Curved Space-Times
• Very Special (de Sitter) Relativity
• Very Special Linear Gravity: A Gauge-Invariant Graviton Mass

Cited by in corpus (3)

• Graviton Mass Bounds in Very Special Relativity from Binary Pulsar's Gravitational Waves
• Infrared Regularization of Very Special Relativity Models
• Generalized Mandelstam-Leibbrandt regularization